


'''simple docstring'''


from math import isqrt







def      snake_case_  (    SCREAMING_SNAKE_CASE__	):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE					:			List[str]							= [True] * max_number
				for i in range(2				, isqrt(max_number - 1	) + 1	):
								if is_prime[i]:
												for j in range(i**2				, SCREAMING_SNAKE_CASE__				, SCREAMING_SNAKE_CASE__	):
																_SCREAMING_SNAKE_CASE					:			Dict							= False

				return [i for i in range(2				, SCREAMING_SNAKE_CASE__	) if is_prime[i]]







def      snake_case_  (    SCREAMING_SNAKE_CASE__ = 10**8	):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE					:			Optional[int]							= calculate_prime_numbers(max_number // 2	)

				_SCREAMING_SNAKE_CASE					:			List[Any]							= 0
				_SCREAMING_SNAKE_CASE					:			Dict							= 0
				_SCREAMING_SNAKE_CASE					:			List[str]							= len(SCREAMING_SNAKE_CASE__	) - 1
				while left <= right:
								while prime_numbers[left] * prime_numbers[right] >= max_number:
												right -= 1
								semiprimes_count += right - left + 1
								left += 1

				return semiprimes_count


if __name__ == "__main__":
				print(F"{solution() = }")








'''simple docstring'''


import os


# All paths are set with the intent you should run this script from the root of the repo with the command
# python utils/check_doctest_list.py
UpperCAmelCase_						:  List[Any]				  =						'.'


if __name__ == "__main__":
				UpperCAmelCase_						:  Any				  =						os.path.join(REPO_PATH, 'utils/documentation_tests.txt')
				UpperCAmelCase_						:  Dict				  =						[]
				UpperCAmelCase_						:  Union[str, Any]				  =						[]
				with open(doctest_file_path) as fp:
								for line in fp:
												UpperCAmelCase_						:  int				  =						line.strip()
												UpperCAmelCase_						:  str				  =						os.path.join(REPO_PATH, line)
												if not (os.path.isfile(path) or os.path.isdir(path)):
																non_existent_paths.append(line)
												all_paths.append(path)
				if len(non_existent_paths) > 0:
								UpperCAmelCase_						:  int				  =						'\n'.join(non_existent_paths)
								raise ValueError(F"`utils/documentation_tests.txt` contains non-existent paths:\n{non_existent_paths}")
				if all_paths != sorted(all_paths):
								raise ValueError('Files in `utils/documentation_tests.txt` are not in alphabetical order.')




